Finite-Element Time-Domain Analysis of Electrically and Magnetically Dispersive Periodic Structures

A formulation is presented for the finite-element time-domain (FETD) analysis of periodic structures that contain electrically and/or magnetically dispersive materials. The formulation is based on the previously developed transformed field variable approach and the Floquet absorbing boundary condition, which are both applicable to arbitrary scan or incident angles. The paper describes an implicit finite-element time-marching equation for the transformed electric field variable coupled with a finite-difference type equation for the evaluation of the transformed magnetic field variable. The technique is applicable to general dispersive materials, although the required convolution calculations can be greatly accelerated when the electric and magnetic susceptibilities can be represented by a pole expansion. Numerical examples are presented to demonstrate the validity and capability of the proposed numerical approach which is effective for the efficient broadband analysis of complex periodic structures such as engineered materials and phased-array antennas.

I. Introduction

The accurate analysis of periodic structures is of considerable importance to the design of phased-array antennas, frequency selective surfaces (FSSs), and engineered materials. Among the various numerical methods, the finite element method is well suited to perform such analyses due to its versatility in geometry and material modeling. Much work has been carried out during the past two decades on the development of the finite element method for modeling three-dimensional, doubly periodic phased arrays for a variety of configurations [1]–[9]. In particular, Jin and Volakis [1] developed the three-dimensional frequency-domain based finite element analysis for infinitely periodic arrays of cavity-backed antennas. McGrath and Pyati [2] and Lucas and Fontana [3] developed a similar method for more general periodic arrays consisting of more complicated antennas, and Eibert et al. [5] applied a special technique to accelerate the evaluation of the periodic Green's function employed in the boundary integral equation for the truncation of the finite element computational domain.